Kish_HP2: Employee Salaries Analysis

Import and Setup

Setup

# loading libraries
library(tidyverse)
library(here)
library(scales)
library(gt)

Import

# locating
here::i_am("analysis/Kish_HP2.qmd")
library(here)

# reading in data
# df was used instead of a longer name for the sake of my sanity in typing
df <- read.csv(here("data/Employee_Salaries.csv"))

Explanation of Data Variables

# Department
# Abbreviation/acronym for the department name. Example: ABS for the Alcohol Beverage Services department

# Department_Name
# the department name for all active, permanent employees of Montgomery County, MD (Maryland)


# Division
# The division for each department. That is, a single department can have multiple divisions and focuses.
# Example: ABS has the divisions that include those of ABS 85 Administrative Services
# and ABS 85 Beer Delivery Operations

# Gender
# the Gender of M and F. Assuming that since this is filings with the government, M is to be the legal sex of the individual M for Male and F for Female.

# Base_Salary
# precise base salaries (including down to the cent) for the individual, at the end of the calendar year.
# this is projected data. Should be accurate, but projection allows for greater flexibiliity.


# Overtime_Pay
# amount of overtime pay an employee/individual received for working beyond what they were required to do


# Longevity_Pay
# Longevity pay gives additional compensation for qualifying employees who have worked for a good deal of time. The longer time that is worked, the greater the longevity pay. Specifics about how long are dealt with in-house.


# Grade
# the standing an employee has within a company. The internal codes for all positions are not provided, but we can safely look at M1, M2, M3, etc. as those are clearly levels of management. There are thousands of grades.

# M4-Senior Manager (Not included in this particular data)
# M3-Middle Manager
# M2-Middle Manager
# M1-First Level Manager

Case Study: Employees of Montgomery County, MD paid in calendar year 2023

Workplace inequalities are a concern to many. We’ll be examining that topic — with the example of reliable and public data from Montgomery County, MD.

The employees in question are all active, permanent employees of Montgomery County, MD (Maryland).

Each employee works in a department, where each department can have multiple divisions.

In addition to one’s guaranteed base pay, an employee could earn overtime pay, longevity pay (when eligible for working at the company for a long time), both (additional compensation), either overtime or longevity pay, or neither.

These forms of pay (specifically, base pay and additional pay) sum to an employee’s total compensation.

Additional detail can be found above in “Explanation of Data Variables” tab.

We will begin by exploring the relationship between base pay and total compensation across all employees.

Then, we will look to see how this relationship develops across gender, management, and department.

Preliminary

First, let’s establish the data that we’ll be looking at

# Computing Total and Additional Compensation
df$Total_Compensation <- df$Base_Salary + df$Overtime_Pay + df$Longevity_Pay
df$Additional_Compensation <- df$Overtime_Pay + df$Longevity_Pay

# Reading Gender as Sex
df <- rename(df, Sex = "Gender")

# str(df)
# checking the datatypes for each variable
# df <- df |> mutate(across(where(is.double), as.integer))
# Double deemed more useful, can change to integer if further analysis needs integer type

# detecting NA Values
sum(is.na(df))

Additional compensation will be the combination of overtime and longevity pay.

Total compensation will be the combination of base pay and additional compensation.

In the data, there are 0 missing values. (Good news!)

Assuming that since this data comes from the public and not the private sphere (and so the data would be collected based on public filings), M is assumed to be the legal sex of the individual — M for Male and F for Female. That is, sex as legality rather than gender as identity seems to be what is implied. Occasionally, the term “gender” might be used here as well to refer to “sex”.

Topic 1 Total Compensation and Overtime

Preliminary Analysis

How many employees are there? How many of them get overtime, longevity, either, or both?

Preliminary Analysis

#each row is a unique employee, for each dataset


# Total Count & cresting Employee number column
Total_Employees <- nrow(df)
df <- mutate(df, Employee = row_number())

# Base Count & Percentage
Employees_Without_Base <- filter(df, Base_Salary == 0.00) 
Employees_With_Base <- anti_join(df, Employees_Without_Base)
Percent_With_Base <- (nrow(Employees_With_Base) / Total_Employees) * 100



# Over Count & Percentage
Employees_Without_Overtime <- filter(df, Overtime_Pay == 0.00)
Employees_With_Overtime <- anti_join(df, Employees_Without_Overtime)
Percent_Overtime <- (nrow(Employees_With_Overtime) / Total_Employees) * 100


# Long Count & Percentage
Employees_Without_Longevity <- filter(df, Longevity_Pay == 0.00)
Employees_With_Longevity <- anti_join(df, Employees_Without_Longevity)
Percent_Longevity <- (nrow(Employees_With_Longevity) / Total_Employees) * 100


# Either Over or Long Count % Percentage
Employees_Without_Over_Long <- filter(df, Overtime_Pay == 0.00 | Longevity_Pay == 0.00)
Employees_With_Over_Long <- anti_join(df, Employees_Without_Over_Long)
Percent_Over_Long <- (nrow(Employees_With_Over_Long) / Total_Employees) * 100

# Add Comp Count % Percentage
Employees_Without_Add_Comp <- filter(df, Additional_Compensation == 0.00)
Employees_With_Add_Comp <- anti_join(df, Employees_Without_Add_Comp)
Percent_Add_Comp <- (nrow(Employees_With_Add_Comp) / Total_Employees) * 100

There are 10291 employees total, where 0 employees have no base salary (100% have a base salary)

Approximately 16.3% have overtime pay, 27.6% have longevity pay, and 16.3% have one or the either, and 66.1% have both.

Diminishing Returns?

Plot Coefficients

Is overtime pay worth it? Does it have diminishing returns? If overtime pay (and other additional compensation) had diminishing returns, we would expect its slope to be less than 1. A slope of greater than 1 indicates that you get more and more total compensation for every bit more overtime and other additional pay you do. A higher slope indicates a greater degree of this scaling — which is desireable!

Preliminary Analysis Coefficients

Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(df))

Over_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Overtime))

Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Longevity))

Over_Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Over_Long))

Add_Comp_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Add_Comp))

Based on the coefficients for the graphs, those who only get base pay have their total compensation scale up the least with those having overtime and longevity pay scaling up the most.

In particular, as is seen in the plots too, overtime pay scales slightly larger than longevity pay.

So, there does seem to be a non-zero difference between the slope of taking on overtime (and getting more pay) + total compensation and the slope of 1 (overtime pay is directly correlational with total compensation)

Plots

Preliminary Analysis Plots

#overall
p <- df |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") +
  geom_smooth(method = "lm")
p

The slope coefficient (intercept and then slope) is 3269.0284279, 1.070269.

Respective Percentage Total Compensation

p2 <- Employees_With_Overtime |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Overtime Pay") +
  geom_smooth(method = "lm")
p2

The slope coefficient (intercept and then slope) is -1.1910607^{4}, 1.3303052.

Respective Percentage Total Compensation

p3 <- Employees_With_Longevity |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Longevity Pay") +
  geom_smooth(method = "lm")
p3

The slope coefficient (intercept and then slope) is -1.1115563^{4}, 1.2845143.

Respective Percentage Total Compensation

p4 <- Employees_With_Over_Long |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Overtime or longevity pay") +
  geom_smooth(method = "lm")
p4

The slope coefficient (intercept and then slope) is -3.2010085^{4}, 1.5664147.

Respective Percentage Total Compensation

p5 <- Employees_With_Add_Comp |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm")
p5

The slope coefficient (intercept and then slope) is -4803.6504064, 1.2194241.

Diminishing Returns? Revisted: Percentages

How much of their total compensation is base + overtime, longevity, either, or both (In terms of percentage?)

Respective Percentage Total Compensation

# addiing to the original df a new column, using mutate, that is the percent of total
# compensation that is each of the relevant factors.

df <- group_by(df, Employee) |>
  mutate(Percent_Over = Overtime_Pay/Total_Compensation)
df$Percent_Over <- round(df$Percent_Over, 3) * 100

df <- group_by(df, Employee) |>
  mutate(Percent_Long = Longevity_Pay/Total_Compensation)
df$Percent_Long <- round(df$Percent_Long, 3) * 100

df <- group_by(df, Employee) |>
  mutate(Percent_Base = Base_Salary/Total_Compensation)
df$Percent_Base <- round(df$Percent_Base, 3) * 100

df <- group_by(df, Employee) |>
  mutate(Percent_Add_Comp = Additional_Compensation/Total_Compensation)
df$Percent_Add_Comp <- round(df$Percent_Add_Comp, 3) * 100

df <- group_by(df, Employee) |>
  mutate(Percent_Over_Long = Base_Salary/Total_Compensation)
df$Percent_Over_Long <- round(df$Percent_Over_Long, 3) * 100

Coefficients of the percentage things

Preliminary Analysis Plots

Percent_Base_Total_lm <- lm(Total_Compensation ~ Percent_Base, 
           data = filter(df))

Percent_Over_Total_lm <- lm(Total_Compensation ~ Percent_Over, 
           data = filter(df))

Percent_Long_Total_lm <- lm(Total_Compensation ~ Percent_Long, 
           data = filter(df))

Percent_Over_Long_Total_lm <- lm(Total_Compensation ~ Percent_Over_Long, 
           data = filter(df))

Percent_Add_Comp_Total_lm <- lm(Total_Compensation ~ Percent_Add_Comp, 
           data = filter(df))

In terms of these slope coefficients, longevity pay has the greatest scaling. Interestingly, the more percentage base pay you have, the less your total compensation! (negative slope!)

Plots

Preliminary Analysis Plots

p6 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Base, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Base", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm")
p6

The slope coefficient (intercept and then slope) is 2.4535346^{5}, -1576.4445085.

Preliminary Analysis Plots

p10 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Over, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Add Comp", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p10

The slope coefficient (intercept and then slope) is 9.0650397^{4}, 1428.4602409.

Preliminary Analysis Plots

p7 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Long, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Long", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm")
p7

The slope coefficient (intercept and then slope) is 9.406297^{4}, 4668.7561887.

Preliminary Analysis Plots

p8 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Over_Long, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Over Long", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm")
p8

The slope coefficient (intercept and then slope) is 2.4535346^{5}, -1576.4445085.

Preliminary Analysis Plots

p9 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Add_Comp, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Add Comp", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p9

The slope coefficient (intercept and then slope) is 8.7709012^{4}, 1576.4445085.

Again, in terms of these slope coefficients, longevity pay has the greatest scaling. Perhaps there are other things going on in that are affecting this (higher skill = higher pay?)

Topic 2 Gender

Gender is one of the most cited inequalities anywhere, let alone the workplace.

We will be going through our previous analysis, but this time separate Male and Female to see if their scalings differ.

The sex with the higher (positive) scaling benefits more from overtime, longevity pay, etc.

This is a simplified analysis that does not control for how much (if at all) each sex accepts these additional forms of compensation (e.g. overtime) — it is at a higher level. That is, it is looking at the resulting inequalities between males and females regardless of how those inequalities came to be.

Source of Income Coefficients, by Gender

Data Coefficients, by Gender

# Base effect on total compensation, by sex
M_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(df, Sex =="M"))
F_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(df, Sex == "F"))

# Over
M_Over_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Overtime, Sex =="M"))
F_Over_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Overtime, Sex == "F"))

# Long
M_Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Longevity, Sex =="M"))
F_Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Longevity, Sex == "F"))

# Over Long
M_Over_Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Over_Long, Sex =="M"))
F_Over_Long_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Over_Long, Sex == "F"))



#Add Comp
M_Add_Comp_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Add_Comp, Sex =="M"))
F_Add_Comp_Base_Total_lm <- lm(Total_Compensation ~ Base_Salary, 
           data = filter(Employees_With_Add_Comp, Sex == "F"))

Percentage Source of Income Coefficients, by Gender

NOTE: ignored in analysis, deemed insignificant to the question of gender

Data Percent Coefficients, by Gender

# Percent Base
Gender_Percentage_M_lm <- lm(Total_Compensation ~ Percent_Base, 
           data = filter(df,Sex =="M"))

Gender_Percentage_F_lm <- lm(Total_Compensation ~ Percent_Base, 
           data = filter(df, Sex =="F"))


# Percent Over
Gender_Percentage_Over_M_lm <- lm(Total_Compensation ~ Percent_Over, 
           data = filter(df, Sex =="M"))

Gender_Percentage_Over_F_lm <- lm(Total_Compensation ~ Percent_Over, 
           data = filter(df, Sex =="F"))



# Percent Long
Gender_Percentage_Long_M_lm <- lm(Total_Compensation ~ Percent_Long, 
           data = filter(df, Sex =="M"))

Gender_Percentage_Long_F_lm <- lm(Total_Compensation ~ Percent_Long, 
           data = filter(df, Sex =="F"))


# Percent Over Long
Gender_Percentage_Over_Long_M_lm <- lm(Total_Compensation ~ Percent_Over_Long, 
           data = filter(df, Sex =="M"))

Gender_Percentage_Over_Long_F_lm <- lm(Total_Compensation ~ Percent_Over_Long, 
           data = filter(df, Sex =="F"))


# Percent Add Comp
Gender_Percentage_Add_Comp_M_lm <- lm(Total_Compensation ~ Percent_Add_Comp, 
           data = filter(df, Sex =="M"))

Gender_Percentage_Add_Comp_F_lm <- lm(Total_Compensation ~ Percent_Add_Comp, 
           data = filter(df, Sex =="F"))

Gender Analysis Plots

Source of Income, by Gender

Gender Plot 1

#overall
p1 <- df |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p1

The slope coefficient (intercept and then slope) for males is 5255.617831, 1.0914173 and for females it is 2325.7268239, 1.0198384.

Gender Plot 2

p2 <- Employees_With_Overtime |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Overtime Pay") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p2

The slope coefficient (intercept and then slope) for males is -1.2171035^{4}, 1.3550508 and for females it is-5720.6699864, 1.1905479.

Gender Plot 3

p3 <- Employees_With_Longevity |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Longevity Pay") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p3

The slope coefficient (intercept and then slope) for males is -1.0675483^{4}, 1.3218743 and for females it is -2616.177079, 1.1207052.

Gender Plot 4

p4 <- Employees_With_Over_Long |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Those with Overtime or longevity pay") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p4

The slope coefficient (intercept and then slope) for males is -3.2236932^{4}, 1.5862565 and for females it is -1.7913256^{4}, 1.3598861.

Gender Plot 5

p5 <- Employees_With_Add_Comp |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm") +
  facet_wrap(~Sex)
p5

The slope coefficient (intercept and then slope) for males is -5492.0835418, 1.2586281 and for females it is -261.9011481, 1.0971166.

It looks like males are consistently getting higher slopes than their counterparts.

p6 <- df |>
  group_by(Employee) |>
ggplot(mapping = aes(x = Percent_Base, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Percent Base", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All those with additional compensation") +
  geom_smooth(method = "lm")
p6

`geom_smooth()` using formula = 'y ~ x'

Topic 3 Management

The data provided was not too clear on the types of jobs each employee had. However, I was able to pick out those jobs dealing with management. Do these jobs follow the trends we saw earlier? Both in terms of additional compensation scaling and men benefiting from this more? Due to limitations in the data (the spread of the managerial data does not allow for proper slope analysis) we will be relying on visuals and summaries.

Management was broken down into categories: where M4-Senior Manager (Not included in this particular data)

M3-Middle Manager M2-Middle Manager M1-First Level Manager

Management Data Data-Tidying

Management Data Tidying

#filter
Management_1 <- filter(df, Grade == "M1")
Management_2 <- filter(df, Grade == "M2")
Management_3 <- filter(df, Grade == "M3")

#combine 
Management_df <- bind_rows(Management_1, Management_2, Management_3)

Is Management Data similar to The original? Are Male and Female equally represented?

Management Data Comparability

# all
Row_Management_df <- Management_df |> nrow()

# M F distinction
Row_M_Management_df <- Management_df |> filter(Sex =="M") |> nrow()
Row_F_Management_df <- Management_df |> filter(Sex =="F") |> nrow() 

# Male Managerial distinction
Row_M_M1_Management_df <-  Management_df |> filter(Grade == "M1") |> filter(Sex =="M") |> nrow()
Row_M_M2_Management_df <- Management_df |> filter(Grade == "M2") |> filter(Sex =="M") |> nrow()
Row_M_M3_Management_df <- Management_df |> filter(Grade == "M2") |> filter(Sex =="M") |> nrow()

# Female Managerial distinction
Row_F_M1_Management_df <- Management_df |> filter(Grade == "M1") |> filter(Sex =="F") |> nrow()
Row_F_M2_Management_df <- Management_df |> filter(Grade == "M2") |> filter(Sex =="F") |> nrow()
Row_F_M3_Management_df <- Management_df |> filter(Grade == "M2") |> filter(Sex =="F") |> nrow()

There are 446 employees in management. 214 of those are male and 232 of those are female.

Between the management levels, males and females seem to be equally represented.

In M1, there are 17 males and 11 females.

In M2, there are 73 males and 74 females.

In M3, there are 73 males and 74 females.

Management Plots

Management Plots

p <- Management_df |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") +
  geom_smooth(method = "lm") +
  facet_wrap(~ Grade)
p

The slopes look pretty similar…

Management Plots

p <- Management_df |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") +
  geom_smooth(method = "lm") +
  facet_wrap(~ Sex)
p

The slopes look pretty even across the sexes too, what if we combined them?

Management Plots

p2 <- Management_df |>
ggplot(mapping = aes(x = Base_Salary, y = Total_Compensation)) +
  geom_point(aes(color = "red")) +
  scale_x_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") +
  geom_smooth(method = "lm") +
  facet_grid(rows = vars(Grade), cols = vars(Sex))
p2

Yeah, the slopes look pretty similar across the charts! Remember, there is not a lot of management specific data, so some lines might appear to have more or less extension than they otherwise would.

Management Summary

Let’s look at the the management data to see some specific numbers that wouldn’t show up in a graph

Comparability

First, let’s see how employees with management jobs compare to employees at large — to see if we picked an okay sample.

Mean Base Salary Management

Management_df |>
  group_by(Sex) |>
summarize(mean = mean(Base_Salary)) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Sex	mean
F	150932.1
M	155994.6

Mean Base Salary All

df |>
  group_by(Sex) |>
summarize(mean = mean(Base_Salary)) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Sex	mean
F	87497.50
M	92382.93

Well, to maybe not too much suprise, the mean base salaries for management are much higher than average.

Mean Total Compensation Management

Management_df |>
  group_by(Sex) |>
summarize(mean = mean(Total_Compensation)) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Sex	mean
F	150968.2
M	157011.8

Mean Total Compensation All

df |>
  group_by(Sex) |>
summarize(mean = mean(Total_Compensation)) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Sex	mean
F	91559.04
M	106083.94

Interestingly too, the mean total compensation salaries for management are much higher than average. Also, it is important to note here that there is little additional compensation above base salary for management, so perhaps this wasn’t the most ideal choice!

Comparability: Sex

Mean Total Compensation Management Male

head(Management_df |>
filter(Sex == "M") |> 
summarize(Total_Compensation) |> 
arrange(desc(Total_Compensation)), 100) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Employee	Total_Compensation
1323	256993.0
591	196059.0
1679	196059.0
1681	196059.0
2060	196059.0
3424	196059.0
7555	196059.0
7569	196059.0
10216	196059.0
10257	196059.0
7799	196040.7
7117	195794.5
501	193460.3
5669	193460.3
2923	191726.0
2017	190784.7
2924	190000.0
3252	183625.7
469	176948.0
1	175873.0
515	175873.0
529	175873.0
572	175873.0
578	175873.0
846	175873.0
1448	175873.0
1458	175873.0
1517	175873.0
1587	175873.0
1618	175873.0
1694	175873.0
1837	175873.0
2053	175873.0
2061	175873.0
2118	175873.0
2296	175873.0
2363	175873.0
3246	175873.0
3445	175873.0
3505	175873.0
3585	175873.0
3587	175873.0
3590	175873.0
3600	175873.0
3632	175873.0
3877	175873.0
5309	175873.0
5668	175873.0
5735	175873.0
7573	175873.0
7760	175873.0
7776	175873.0
7856	175873.0
7859	175873.0
9684	175873.0
10155	175873.0
10215	175873.0
10224	175873.0
10268	175872.4
364	175861.2
3568	175409.9
6413	175273.1
7594	175099.4
844	174796.6
1688	174396.4
1682	174093.2
7802	172457.9
7814	170084.7
3608	169873.5
7777	168747.6
5147	168258.1
2062	168234.0
6277	167350.4
9030	165543.8
6165	158075.4
437	157272.3
919	155976.0
3910	154769.8
1360	154508.5
2348	154277.8
7870	154201.7
7682	153930.2
239	152940.0
1412	152940.0
1520	152940.0
1593	152940.0
1612	152940.0
1619	152940.0
1635	152940.0
1764	152940.0
1798	152940.0
2021	152940.0
2069	152940.0
2077	152940.0
2298	152940.0
2318	152940.0
2323	152940.0
2371	152940.0
3247	152940.0
3266	152940.0

Mean Total Compensation Management Female

head(Management_df |>
filter(Sex == "F") |> 
summarize(Total_Compensation) |> 
arrange(desc(Total_Compensation)), 100) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Employee	Total_Compensation
859	196059.0
1389	196059.0
3584	196059.0
7122	196059.0
7818	196059.0
7558	194520.4
5680	188679.9
7752	185609.7
722	180704.1
3599	179833.0
606	179259.9
536	178510.6
521	177064.1
537	175873.0
555	175873.0
584	175873.0
593	175873.0
1308	175873.0
1557	175873.0
1669	175873.0
1680	175873.0
1996	175873.0
2067	175873.0
2775	175873.0
3458	175873.0
3586	175873.0
3595	175873.0
3598	175873.0
3648	175873.0
5156	175873.0
5158	175873.0
5315	175873.0
5488	175873.0
5788	175873.0
6065	175873.0
6086	175873.0
7036	175873.0
7687	175873.0
7779	175873.0
8864	175873.0
9861	175873.0
10129	175873.0
10162	175873.0
10206	175873.0
10174	175867.1
10159	175259.7
604	174876.5
6275	174165.9
6308	174165.9
834	174000.0
3421	172415.2
608	172026.6
7797	171540.0
10212	171540.0
9712	171520.4
9859	170930.7
6064	170203.8
824	169159.0
8977	169114.8
7745	168128.4
6066	167791.7
7815	167314.0
5802	167227.2
115	166140.0
9721	165998.0
5164	164333.0
8697	158007.4
5163	157550.0
5507	156050.5
7559	155747.5
1670	153000.7
465	152940.0
471	152940.0
504	152940.0
579	152940.0
1306	152940.0
1433	152940.0
1477	152940.0
1547	152940.0
1566	152940.0
1609	152940.0
1961	152940.0
2008	152940.0
2036	152940.0
2066	152940.0
2364	152940.0
3387	152940.0
3577	152940.0
3589	152940.0
3645	152940.0
3893	152940.0
4066	152940.0
5761	152940.0
6483	152940.0
6498	152940.0
6574	152940.0
6835	152940.0
7664	152940.0
7698	152940.0
8973	152940.0

Sorry for the scrolling, but in terms of the “glass-ceiling” — it seems like the top earners are males, with female compensation dropping off more quickly than male compensation

Topic 4: Department

Was our data consistent among all departments? Are one or a few departments possible skewing the data (and the above discussed scaling?)

Department Plots

Focus: Sex

Management Summary

p2 <- df |>
ggplot(mapping = aes(x = Department, y = Total_Compensation)) +
  geom_point(aes(color = Sex, shape = Sex, size = Base_Salary)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") 
p2

It seems like M and F are pretty okay in terms of the spread. FRS and POL looks male dominated and HHS looksfemale dominated.

Focus: Percent Base Salary & Additional Compensation

Base Salary

Management Summary

p2 <- df |>
ggplot(mapping = aes(x = Department, y = Total_Compensation)) +
  geom_point(aes(color = Percent_Base, size = Sex)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") 
p2

COR, FRS, and POL stick out as having higher total compensation, and this compensation (shown in dark blue) becomes higher at the point where it no longer is because of their base salary as much.

Additional Compensation

Management Summary

p2 <- df |>
ggplot(mapping = aes(x = Department, y = Total_Compensation)) +
  geom_point(aes(color = Percent_Add_Comp, size = Sex)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") 
p2

That is, same as above, you can see COR, FRS, and POL start to have additional compensation right where they start to get above the rest.

Focus: Combine them! (Gender & Percent Base Salary)

Management Summary

p2 <- df |>
ggplot(mapping = aes(x = Department, y = Total_Compensation)) +
  geom_point(aes(color = Percent_Base, shape = Sex, size = Base_Salary)) +
  scale_y_continuous(labels = label_number(suffix = " K", scale = 1e-3)) +
    labs(x = "Base Salary", y = "Total Compensation", title = "Base Salary vs. Total Compensatory for All Employees") 
p2

Here’s an intersting visual showing the same information as the two previous — but here again we still se COR, FRS, and POL sticking out.

Those three lines with lower percent bases and higher total comp are COR FRS and POL.

Management Summary

#   Correction and Rehabilitation
head(filter(df, Department == "COR"), 1) |>
  select(1:2) |>gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Department	Department_Name
862
COR	Correction and Rehabilitation

Management Summary

head(filter(df, Department == "FRS"), 1) |>
  select(1:2)|> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Department	Department_Name
3690
FRS	Fire and Rescue Services

Management Summary

head(filter(df, Department == "POL"), 1) |>
  select(1:2) |> gt()|>
  opt_row_striping() |> 
  opt_stylize(style = 4, color = "red")

Department	Department_Name
7918
POL	Department of Police

Based on what the three departments are, as shown in the tables above, do you have any idea why they would stick out? (I don’t have an hypothesis, personally)

Conclusion

We saw evidence that there is a lack of diminishing returns for getting additional compensation

Moreover, males tend to experience less diminishing returns than their counterparts.

The gender of participants seems to be pretty consistent across all departments, and three departments stick out for how they compensate their employees.

Management is not too much like the entire data in terms of mean base salary and mean total compensation, but the slopes of the lines do not look too radical